Partial projective representations and partial actions.

*(English)*Zbl 1211.20016The purpose of the present article is to define partial projective representations of groups in analogy with the classical representation theory. This notion is closely connected with the notions twisted partial products and twisted partial actions [see M. Dokuchaev, R. Exel and J. J. Simón, J. Algebra 320, No. 8, 3278-3310 (2008; Zbl 1160.16016)].

First, the authors give the necessary information about projective representations of semigroups and their factor sets [see B. V. Novikov, Dopov. Akad. Nauk Ukr. RSR, Ser. A 1979, 472-475 (1979; Zbl 0411.20047)]. After that they define equivalent factor sets, product of factor sets and Schur multiplier of a semigroup with identity. So the authors define partial projective representations of a group by means of projective representations of a semigroup which is associated with the group. It is given another definition, which is independent of semigroups. Later in the paper is studied the structure of the factor sets of partial projective representations. The connections between the projective partial representations and the twisted partial actions are also investigated.

First, the authors give the necessary information about projective representations of semigroups and their factor sets [see B. V. Novikov, Dopov. Akad. Nauk Ukr. RSR, Ser. A 1979, 472-475 (1979; Zbl 0411.20047)]. After that they define equivalent factor sets, product of factor sets and Schur multiplier of a semigroup with identity. So the authors define partial projective representations of a group by means of projective representations of a semigroup which is associated with the group. It is given another definition, which is independent of semigroups. Later in the paper is studied the structure of the factor sets of partial projective representations. The connections between the projective partial representations and the twisted partial actions are also investigated.

Reviewer: S. V. Mihovski (Plovdiv)

##### MSC:

20C25 | Projective representations and multipliers |

20M30 | Representation of semigroups; actions of semigroups on sets |

16S35 | Twisted and skew group rings, crossed products |

##### Keywords:

representations of semigroups; partial projective representations of groups; Schur multipliers; factor sets; twisted partial actions
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\textit{M. Dokuchaev} and \textit{B. Novikov}, J. Pure Appl. Algebra 214, No. 3, 251--268 (2010; Zbl 1211.20016)

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